In this context, mortgaged means to give up or sacrifice something valuable (in this case, time) in exchange for something else, often with the implication that it comes at a significant cost. The sentence suggests they would have traded a precious part of their limited individual life for something else, possibly a commitment or responsibility.

Metaphorically, it means they have sacrificed their freedom to do as they please by accepting some burdensome obligation.

This is an oddly phrased answer but mortgage is the loan from a bank (or other) to buy a house. So mortgages means saved away/put away/ given to.